c.density-cf is a smoothness condition for the corresponding density. By [1]}, it is equivalent to \((\sum _{j=1}^n X_j,\sum _{j=1}^n X_j^2)\) 
having bounded densities for \(n\)  sufficiently large.
In this case, \(p_{d}=0\)  (see eq.lebesgue-dec) holds necessarily because any discrete part cannot not vanish when summing up i.i.d. random variables (see [2]}).
c.density-cf implies Cramér condition (see [3]}), but it does not imply non-singularity and neither does non-singularity imply c.density-cf (see [1]}).
